Tuesday, October 7, 2014

Temperature Measurement Fails

The following diagram illustrate temperature measurement,


where  \(T\)  is the total amount of energy distributed among  \(N\)  atoms.  When thermal equilibrium is reached with another body of  \(n\)  atoms,  we have a measure,

\(K=\cfrac{T+T_o}{N+n}\)

obviously,

\(K=\cfrac{T+T_o}{N+n}\ne\cfrac{T}{N}\)

When   \(T\)  is large or  \(N\)  is large then

\(\cfrac{T+T_o}{N+n}\approx\cfrac{T}{N}\)

but when  \(T\)  is small or  \(N\)  is small, the measurement fails.